In parallel to the growing capabilities of optical fibre to carry ultra-high speed digital information, satellite communication systems undoubtedly represent a big success thanks to their ability to efficiently broadcast digital multi-media information over very large areas. A notable example is the so-called direct-to-home (DTH) digital television broadcasting. Satellite systems also provide a unique way to complement the terrestrial infrastructure. This is the case, for instance, for satellite news gathering systems linking mobile TV stations to the central production facility or the multi-media satellite systems currently under development.
These systems, either existing or in preparation for the near future, are likely to require higher bit rates than before, thus extracting as many bits per second as possible from the available bandwidth becomes a necessity. This calls in turn for the use of higher-order modulations, combined with state-of-the-art coding schemes.
It is well known that for satellite channels the constellation 16-QAM (Quadrature Amplitude Modulation), although providing twice the spectral efficiency of the widely used QPSK (Quadrature Phase Shift Keying), suffers greatly from satellite amplifier non-linearity effects. To-day, trellis coded (TC) 16-QAM has been adopted for high speed satellite links (e.g. TV contributions) at the cost of higher operating link signal-to-noise ratios (Eb/No increase of typically 4–4.5 dB) and a larger operational amplifier output back-off (OBO) (typically 3 to 5 dB). See for instance M. Cominetti and A. Morello, Digital Video Broadcasting over satellite (DVB-S): a system for broadcasting and contribution applications, Int. Jour. on Satellite Commun., 2000, No. 18, pp. 393–410.
It has been observed that the distance between pairs of constellation points is far from uniform and a few points are indeed very close to each other, thereby significantly reducing the minimum distance between constellation points. The current demand for bandwidth efficient high-speed satellite communication links calls for the development of more effective alternatives to 16-QAM. An alternative would be the use of 16-PSK, which is known to be more resilient to non-linear channels. However, the signal-to-noise ratio required for this modulation is higher than that of 16-QAM, removing some of its attractiveness.
The topic of high-order constellation optimization has already been addressed for band-limited linear channels. To the inventors' knowledge however, there are few references in the literature dealing with 16-ary constellation optimization over non-linear channels. Former work related to digital modulation techniques with spectral efficiencies up to 3 bit/s/Hz in non-linear satellite channels showed that 16-QAM does not compare favorably with either TC 16-PSK or uncoded 8-PSK. As an example, S. G. Wilson, H. A. Sleeper II, P. J. Schottler and M. T. Lyons (Rate ¾ Convolutional Coding of 16-PSK: Code Design and Performance Study, IEEE Trans. on Commun., Vol. COM-32, No. 12, December 1984) pointed out that rate-¾ TC 16-PSK gains only a few tenths of a dB over uncoded 8-PSK in a typical satellite channel, assuming perfect carrier phase and clock timing recovery, so that the additional complexity inherent in coded 16-PSK system does not appear to be justified. Also, E. Biglieri (High-Level Modulation and Coding for Nonlinear Satellite Channels, IEEE Trans. on Commun. N. 5, May 1984) performed a comparison between TC 16-QAM and 16-PSK systems over non-linear channels, concluding that 16-PSK outperforms 16-QAM, but the author explicitly excluded the possibility of pre-distorting the signal constellation to counteract non-linear distortions.
A possible improvement for TC 16-QAM exploitation over non-linear satellite channels was proposed by R. De Gaudenzi and M. Luise, in Design and Analysis of an All-Digital Demodulator for Trellis Coded 16-QAM Transmission over a Nonlinear Satellite Channel, IEEE Trans. on Comm., Vol. 43, No. 2/3/4, February/March/April 1995, part I. In this reference it was shown that through trellis decoder metric ad-hoc computation the bit error rate (BER) performance can be improved by about 2 dB compared to conventional TC-16-QAM. However, the post-compensation provided by the trellis decoder metric computation does not prevent the losses due to the distorted constellation shape caused by the High Power Amplifier (HPA).
The purpose of the present invention is to optimize the transmission of digitally modulated signals on non-linear channels rather than only attempt to compensate the satellite non-linearity effects a posteriori. The intuition for the present invention follows the experimental observation of the 16-QAM-constellation distortion caused by the HPA. The challenge here is to combine coding efficiency with the required coding rate flexibility and simple matching to the demodulator. This approach is expected to provide an appreciable advantage in terms of overall efficiency compared to more conventional solutions.